Action Var: 1 DOF System, Ellipse Path in Phase-Space

[quasar987]

Suppose a 1 degree of freedom system. Then, the action variable J is defined by

$$J\equiv\oint p(q)dq$$

where the integral is taken over a period of p(q). What shall this period be in the case of say, an harmonic oscillator, where the path in phase-space is an ellipse and hence p(q) is not even single-valued?

 

[George Jones]

Suppose a 1 degree of freedom system. Then, the action variable J is defined by

$$J\equiv\oint p(q)dq$$

where the integral is taken over a period of p(q). What shall this period be in the case of say, an harmonic oscillator, where the path in phase-space is an ellipse and hence p(q) is not even single-valued?

Parametrize the ellipse in the standard way, and integrate over one period.

 

[quasar987]

Dang it. This is what I tought about doing in my exam too but I had no more time when the idea finally hit me. Thanks GJ.